Let's simplify the expression \( 5(0.5k - 1) + 2(0.4 - k) \).
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Distribute \( 5 \) in the first term: \[ 5(0.5k - 1) = 5 \cdot 0.5k - 5 \cdot 1 = 2.5k - 5 \]
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Distribute \( 2 \) in the second term: \[ 2(0.4 - k) = 2 \cdot 0.4 - 2 \cdot k = 0.8 - 2k \]
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Now, combine the results from the two distributions: \[ 2.5k - 5 + 0.8 - 2k \]
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Combine like terms (the \( k \) terms and the constant terms):
- For the \( k \) terms: \( 2.5k - 2k = 0.5k \)
- For the constant terms: \( -5 + 0.8 = -4.2 \)
Thus, the simplified expression is: \[ 0.5k - 4.2 \]
If you'd like a specific numerical value, please provide a value for \( k \). Otherwise, the final answer in decimal form is: \[ 0.5k - 4.2 \]